For some time apparatuses have been known for objectively measuring the visual defects of the patient, defects that are indeed known as aberrations. The apparatuses or devices used for this purpose are called aberrometers. The derivation of aberrations is equivalent to measuring the wave front coming out from the eye coming from a sharp light source arranged on the fovea. By wave front it is meant the equiphase surface of the light wave coming out from the eye.
In general the methods known up to now for measuring the wave front mainly provide for the use of sensors of two different families. The first comprises sensors adapted to estimate the aberration of the wave front from the interference pattern formed between the wave front itself and a translated version thereof. The second, on the other hand, bases its operation on the geometric optics and—given the dynamics of aberrations that it is able to measure—is the one most used in ophthalmology.
Using a rough schematisation, all of the tools adapted for measuring and characterising the reflective defect, whether they are simple auto-refractometers or more complex aberrometers, have:                1. a projection channel—the purpose of which is to create on the retina a static or dynamic light pattern—depending on the aberrometer principle used, the reflected light of which can operate as emitter;        2. an observation channel at the end of which the wave front sensor is arranged.        
Taking FIG. 1 as reference, these two macro blocks are indicated with A and B.
The projection channel A comprises a light source Sa (static or dynamic, in any case able to project a point or pattern on the retina of the patient), optical elements La such as lenses or diaphragms adapted to make the appropriate projection of the light radiation produced by the source Sa, and possibly elements adapted for generating light patterns, or opto-mechanical elements adapted for moving and/or scanning images of the light source.
The observation channel B is able to collect the light projected by the projection channel A. The wave front sensor WFs and its operation are the key element of the observation channel B. Such an element, indeed, diversifies and characterises the instrument and determines its performance. Considering the wave front sensors developed up to now, all of them have a focusing optic Lb that receives the optical observation beam, for example deviated laterally by a suitable beam splitter Bc arranged on an optical axis of an eye and the retina of which is indicated with R. The optic Lb is adapted to transport the information of the wave front and focus it on a light sensor CCDb. The electrical output of the sensor is transmitted and processed by processing means in order to obtain the morphology of the wave front and the measurement of the refractive error usually through fitting algorithms of the normals of the wave front.
According to the Tscherning method the aberrometer measures the aberration of the wave front as a consequence of the first passing in the ocular medium, i.e. in the image space of the eye. A grid is projected by the projection channel and the observation channel observes the deformation of such a grid on the retina thus obtaining information on the ocular aberrations. A common variant of such a system, instead of projecting a grid on the retina, projects a set of points one after the other at great speed on parallel rays, making it simpler than the original Tscherning method to detect the spots and their deviation with respect to the ideal position.
Other types of aberrometer base their operation on the retinoscopy method, using the same operating principle as the ophthalmological examination of the same name. Retinoscopy consists of observing the apparent movement carried out by the reflected red of the ocular base; the reflection is visible in the pupil field when the eye is illuminated by a flat slit of light rays coming from infinity that is moved in a direction perpendicular to it. If the eye is myopic, the retinal image will have the image of the slit defocused and moved in a position opposite that of entry. If the eye is hypermetropic, the retinal image will have the image of the slit defocused on the same side as the entry position. The extent of the displacement will be proportional to the extent of ametropia that is measured.
The most popular wave front sensor used to detect aberrations in the human eye is, however, the Hartmann-Shack sensor (HSWS). With reference to FIGS. 2a and 2b, in this case an array of lenses is arranged with the same focal and the same diameter D1 in a plane conjugated with the entry pupil of the system for which one wishes to detect the aberrations, so as to separately focus small portions of the wave front on the same image sensor.
It can be seen from the aforementioned figures how in the case of a flat wave front incident on the lenses (FIG. 2a), they will produce images with equally spaced barycentres on the plane of the detector whereas, in the case of an aberrated wave front (FIG. 2b), the local tilt of the portion of wave incident on the i-th lens of the grid will produce a movement of the barycentre of the i-th image. The simplest way to quantitatively measure this signal is to assign a quad-cell (2×2 matrix of photosensitive elements) to each sub-opening. The following quantities are defined
                              ∂          W                          ∂          x                    ∝              S        x              =                            I          2                +                  I          4                -                  I          1                -                  I          3                                      I          1                +                  I          2                +                  I          3                +                  I          4                      ;                              ∂          W                          ∂          y                    ∝              S        y              =                            I          1                +                  I          2                -                  I          3                -                  I          4                                      I          1                +                  I          2                +                  I          3                +                  I          4                    where Ii indicates the intensity recorded by the i-th element of the quad-cell. In the absence of aberrations the image produced will be arranged symmetrically over the four elements, and therefore Sx=Sy=0; in the presence of aberration it is simple to show that Sx and Sy will be different from zero and proportional to the local spatial derivatives of the incident wave front (in the two directions of the plane).
According to all of the previous methods the wave front is obtained from the analysis of an image conjugated to the retinal plane.
Yet another type of sensor is the pyramid wave front sensor (PWS), which bases its functionality essentially on a revisitation of the Foucault knife-edge test, well known to the man skilled in the art. Such a test consists of the following steps:                1) generating a wave front from a point-shaped source;        2) inserting an opaque element into the focus of the optics system to observe what pattern the insertion of a knife creates.        
Taking FIG. 3 as reference in this case, it is shown how in a wave front affected by spherical aberration the rays close to the optical axis are focused on the right of the knife k, i.e. past it, and generate a central distribution, whereas the peripheral ones are focused at a shorter distance and generate an external distribution. Like in the case of the spherical aberration, more common aberrations generate recognisable distributions, and in this way it is generally possible to determine the dominant aberration in the optics system under examination. The use of such a sensor for the purposes of measuring the human eye (which may or may not be coupled with a closed feedback system consisting of adaptive optics) has been used and studied by Iglesias and Ragazzoni in document WO2004025352. What is therein proposed is, first of all, to replace the knife with a square-based pyramid with the vertex in the same position as the knife, actually obtaining the equivalent of two simultaneous Foucault tests in a direction x and in a direction y. With reference to FIG. 4 and to the configuration indicated in it, the entering wave front creates on the CCD four images of the conjugated pupil the light intensity of which depends on the local variation of the wave front itself.
Moreover, if the operating principle of a Foucault knife is considered, it can be worked out that either lit or unlit areas become formed on the CCD, depending on whether the rays destined to such an area are or not interrupted by the presence of the knife. Every known aberration is associated with a recognisable pattern but the extent of the aberration cannot be detected: indeed, two defects of different size but the same shape generate the same distribution on the CCD. With reference to FIGS. 5a-5c, a wave front affected by 1 μm of spherical aberration (exemplified by the representation of FIG. 5a) generates a pattern like that of FIG. 5b, but the same pattern would be generated for example by a wave front affected by 10 μm of spherical aberration.
It is proposed by the same Ragazzoni, with reference to FIG. 3, to overcome this obstacle, to set the knife in motion with oscillating motion of a certain amplitude and so that the period of such oscillation is equal to the exposure time of the sensor. What is thus formed is no longer a “2-level” image but one such as to show a gradient of greys from white to black in which the value of grey is proportional to the local variation of the wave front (called local tilt) and to the size of the oscillating motion. It can be demonstrated that the introduction of such a concept, called modulation of the knife, allows the derivatives in x and in y of the wave front to be made measurable through the following formulae:
                              ∂          W                          ∂          x                    ∝              S        x              =                            I                      1            ⁢            x                          -                  I                      2            ⁢            x                                                I                      1            ⁢            x                          +                  I                      2            ⁢            x                                ;                              ∂          W                          ∂          y                    ∝              S        y              =                            I                      1            ⁢            y                          -                  I                      2            ⁢            y                                                I                      1            ⁢            y                          +                  I                      2            ⁢            y                              Where:                I1x represents the light intensity recorded on the point to be measured of the pupil determined by the knife k in horizontal motion and with k arranged to cover the left part of the beam at rest;        I2x represents the light intensity recorded on the point to be measured of the pupil determined by the knife k in horizontal motion and with k arranged to cover the right part of the beam at rest;        I1y represents the light intensity recorded on the point to be measured of the pupil determined by the knife k in vertical motion and with k arranged to cover the bottom part of the beam at rest;        I2y represents the light intensity recorded on the point to be measured of the pupil determined by the knife k in vertical motion and with k arranged to cover the top part of the beam at rest.In the case of it being carried out through a pyramid-shaped prism, such formulae become:        
                              ∂          W                          ∂          x                    ∝              S        x              =                            I          2                +                  I          4                -                  I          1                -                  I          3                                      I          1                +                  I          2                +                  I          3                +                  I          4                      ;                              ∂          W                          ∂          y                    ∝              S        y              =                            I          1                +                  I          2                -                  I          3                -                  I          4                                      I          1                +                  I          2                +                  I          3                +                  I          4                    where Ii indicates the light intensity recorded on the point to be measured of the i-th pupil determined by the pyramid. Again with reference to FIG. 5, a wave front affected by 1 μm of spherical aberration, schematised by the same representation of FIG. 5a in this way generates a similar pattern to that of FIG. 5c. 
It is also demonstrated that Sx and Sy are proportional to the local spatial derivatives of the incident wave front with a proportionality factor also linked to the size of the modulation. Such relationships are very similar to what is found for HSWS, despite differences between the two systems that will be discussed hereafter.
In the patent document mentioned above, as well as for the first time hypothesising the use of this type of sensor for measuring the total aberration of an eye, it is made clear how the modulation can be avoided provided that a source is used that is not point-shaped but suitably extended.
Indeed, it is hypothesised to leave the pyramid static and to “oscillate the field” above the pyramid. A situation very similar to this is that of creating an extended object. It is thus shown how an optics system, in which the source is no longer point-shaped but extended and incoherent, equally makes it possible to measure the derivatives in x and in y of the wave front through a formula absolutely analogous to the one outlined above but with a proportionality factor linked no longer to the modulation but to the size of the spot on the pyramid, and consequently to the size of the spot on the retina A.
With such a clarification it can be asserted that:
                    ∂        W                    ∂        x              =          α      ⁢                          ⁢      Δ      ⁢                                    I            2                    +                      I            4                    -                      I            1                    -                      I            3                                                I            1                    +                      I            2                    +                      I            3                    +                      I            4                                ;                    ∂        W                    ∂        y              =          α      ⁢                          ⁢      Δ      ⁢                                    I            1                    +                      I            2                    -                      I            3                    -                      I            4                                                I            1                    +                      I            2                    +                      I            3                    +                      I            4                              
Programmable elements equipped with fitting algorithms of the normals are hence able to reconstruct the wave front error or vergence error.